Lecture 16 Magnetic Fields& Force General Physics II, Lec 16, By/ T.A. Eleyan

Torque on a Current Loop Imagine a current loop in a magnetic field as follows: B I b a a/2 F In a motor, one has “N” loops of current General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Example: A circular loop of radius 50.0 cm is oriented at an angle of 30.0o to a magnetic field of 0.50 T. The current in the loop is 2.0 A. Find the magnitude of the torque. 30.0o B General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Galvanometer Device used in the construction of ammeters and voltmeters. General Physics II, Lec 16, By/ T.A. Eleyan

Galvanometer used as Ammeter Typical galvanometer have an internal resistance of the order of 60 W - that could significantly disturb (reduce) a current measurement. Built to have full scale for small current ~ 1 mA or less. Must therefore be mounted in parallel with a small resistor or shunt resistor. Galvanometer 60 W Rp General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Galvanometer used as Voltmeter Finite internal resistance of a galvanometer must also addressed if one wishes to use it as voltmeter. Must mounted a large resistor in series to limit the current going though the voltmeter to 1 mA. Must also have a large resistance to avoid disturbing circuit when measured in parallel. Galvanometer 60 W Rs General Physics II, Lec 16, By/ T.A. Eleyan

Motion of Charged Particle in magnetic field Consider positively charge particle moving in a uniform magnetic field. Suppose the initial velocity of the particle is perpendicular to the direction of the field. Then a magnetic force will be exerted on the particle and make follow a circular path. General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan The magnetic force produces a centripetal acceleration. The particle travels on a circular trajectory with a radius: What is the period of revolution of the motion? The frequency General Physics II, Lec 16, By/ T.A. Eleyan

Example : Proton moving in uniform magnetic field A proton is moving in a circular orbit of radius 14 cm in a uniform magnetic field of magnitude 0.35 T, directed perpendicular to the velocity of the proton. Find the orbital speed of the proton. General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Example: If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion? v r x General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan [Q]: Consider the mass spectrometer. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m=2.18×10-26 kg. General Physics II, Lec 16, By/ T.A. Eleyan

Example: Mass Spectrometer Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion? Key Idea: The uniform magnetic field forces the ion on a circular path and the ion’s mass can be related to the radius of the circular trajectory. General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Cyclotrons A cyclotron is a particle accelerator The D-shaped pieces (descriptively called “dees”) have alternating electric potentials applied to them such that a positively charged particle always sees a negatively charged dee ahead when it emerges from under the previous dee, which is now positively charged General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan The resulting electric field accelerates the particle Because the cyclotron sits in a strong magnetic field, the trajectory is curved The radius of the trajectory is proportional to the momentum, so the accelerated particle spirals outward General Physics II, Lec 16, By/ T.A. Eleyan

Example: Deuteron in Cyclotron Suppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron (m=3.34 10-27kg)? General Physics II, Lec 16, By/ T.A. Eleyan

General Physics II, Lec 16, By/ T.A. Eleyan Example Suppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the kinetic energy of the deuterons in this cyclotron when they travel on a circular trajectory with radius R (m=3.34 10-27kg, B=1.57 T)? A) 0.9 10-14 J B) 8.47 10-13 J C) 2.7 10-12 J D) 3.74 10-13 J General Physics II, Lec 16, By/ T.A. Eleyan